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The Numerical Methods of Quantum Zakharov Equations

Author: LiYong
Tutor: WangJian
School: Shanghai Jiaotong University
Course: Computational Mathematics
Keywords: Zakharov quantum effect energy-preserving dif-ference scheme Predictor-Corrector scheme
CLC: O241.82
Type: Master's thesis
Year: 2012
Downloads: 19
Quote: 0
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Abstract


In this paper, we mainly discuss two numerical solutions of quantum Zakharovequations: energy-preserving difference scheme and Predictor-Corrector scheme. Forenergy-preserving difference scheme, we firstly construct the numerical scheme, andtheoretically prove that this scheme meets the conservation law. Based on this, weprove the stability and convergence of this scheme. Then we introduce the Predictor-Corrector scheme, and construct the Predictor-Corrector scheme for the energy-preserv-ing difference scheme above. Also we prove the conservation law of it. Finally, forthe above two schemes, we do the numerical experiments, and compare the numericalsolution and exact solutions results, which show that the two schemes can have highaccuracy, and be good.

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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